{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:26:20Z","timestamp":1775838380533,"version":"3.50.1"},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4394,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A computably enumerable (c.e.) degree is a <jats:italic>maximal contiguous degree<\/jats:italic> if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the Turing degrees in general. Finally we note that the construction of a maximal contiguous degree can be modified to answer a question of Walk about the array computable degrees and a question of Li about isolated formulas.<\/jats:p>","DOI":"10.2178\/jsl\/1190150052","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:12:10Z","timestamp":1197555130000},"page":"409-437","source":"Crossref","is-referenced-by-count":5,"title":["Maximal contiguous degrees"],"prefix":"10.1017","volume":"67","author":[{"given":"Peter","family":"Cholak","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rod","family":"Downey","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen","family":"Walk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200010070_ref024","first-page":"921","volume":"48","author":"Stob","year":"1983","journal-title":"Wtt-degrees and t-degrees of r.e. sets"},{"key":"S0022481200010070_ref022","unstructured":"Slaman Theodore A. and Woodin W. Hugh [To appear], Defining the double jump, To appear."},{"key":"S0022481200010070_ref021","unstructured":"Slaman Theodore [1993], Open questions in recursion theory, Continuely updated since 1993, http:\/\/math.berkeley.edu\/~slaman."},{"key":"S0022481200010070_ref020","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/257\/04040"},{"key":"S0022481200010070_ref018","volume-title":"Classical recursion theory","author":"Odifreddi","year":"1989"},{"key":"S0022481200010070_ref017","first-page":"241","volume-title":"Proceedings of the London Mathematical Society. Third Series","volume":"77","author":"Nies","year":"1998"},{"key":"S0022481200010070_ref015","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-98-01800-5"},{"key":"S0022481200010070_ref003","first-page":"41","volume-title":"Algebra and analysis (Kazan, 1994)","author":"Cooper","year":"1996"},{"key":"S0022481200010070_ref025","unstructured":"Walk Stephen M. 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